Isothermal Perturbations Research Articles

U–Pb apatite geochronology shows multiple thermal overprints within the Neoarchean foreland basement of the Faroe–Shetland Terrane

The Neoarchean foreland basement of the Faroe–Shetland terrane (FST) displays abundant evidence for isotopic resetting of U–Pb systems in apatite between c. 1800 and 200 Ma, interpreted to result from episodic heating pulses associated with regional-scale tectonic events. Major apparent age peaks of c. 1800–1600 Ma broadly correspond to the timing of Nagssugtoqidian–Laxfordian orogenesis >225 km further south. These are thought to reflect widespread heating during late- to post-orogenic delamination that affected a wide area of the orogenic foreland and resulted in a low to middle greenschist-facies static overprint, affecting much of the FST basement. Late- to post-orogenic delamination might also account for major apparent age peaks at c. 1300–1100, 800 and 500–400 Ma, corresponding to, respectively, Grenvillian, Knoydartian and Caledonian orogenic events. However, east-dipping seismic reflectors in the basement west of Shetland may represent the northward extension of the Grenvillian Outer Hebrides Thrust (Zone) and/or Caledonian thrusts and so perturbation of isotherms during west-directed thrusting could therefore also account for these apparent age peaks. Minor apparent age peaks of c. 700, 600, 350 and 200 Ma are most easily interpreted as resulting from enhanced heat flux that accompanied periods of crustal extension prior to and following the Caledonian orogeny.

Mechanism of adsorption of actives onto microporous functionalised calcium carbonate (FCC)

Microporous ‘functionalised’ calcium carbonate (FCC) has potential for use as a carrier for the controlled release of ‘actives’, by permeation and diffusion. We have investigated the nature of the FCC surface and the mechanism of adsorption of two typical actives, namely the anti-inflammatory drug aspirin and the flavour compound vanillin, from chloroform and aqueous ethanolic solutions. There is indirect evidence from the quantitative perturbation of Toth isotherms that their adsorption is hindered by a stagnant diffusion layer of water trapped in the micro-porosity of the FCC. To complement previous studies of the surface of FCC, it was also tested with the cationic probe benzyltrimethylammonium bromide and the anionic probe sodium 2-naphthalenesulphonate. Experimental procedures were validated by comparison with adsorption onto ground calcium carbonate and high surface area talc.

3D perturbations in an isothermal self-similar flow

We explore three-dimensional (3D) isothermal perturbation structures in a non-linear dynamic background of self-gravitating isothermal radial flow with spherical symmetry. The overall flow then appears quasi-spherically symmetric. Here, the dynamic background radial flow describes a self-similar evolution with a central/final free-fall asymptotic solution and a faraway/initial flow but without involving the sonic critical line (SCL). As transients peter out, 3D perturbations can consistently emerge and evolve in a self-similar manner with angular variations separated out in terms of spherical harmonics and with x = r/(at) as the independent self-similar variable where r, t and a are the radius, time and isothermal sound speed, respectively. Independent asymptotic perturbation solutions in large and small x regimes are derived analytically. Global 3D perturbation solutions are constructed numerically for sensible asymptotic solutions. The fifth-order perturbation equations have solutions of four curl-free modes and one vortex mode, with the former identified as multipole and antimultipole modes, P 1 and P 2 modes, respectively. Of the five solutions, four are of potential astrophysical interest and can be utilized for benchmarking numerical codes and simulation results. Our results show that perturbations may or may not grow in a free-fall manner, depending on initial perturbations in mass and velocity distribution. We also find that vortex mode can be converted to other modes during a collapse, and in the l = 1 case, mode conversion will serve to produce a gravitational dipole. For self-similar solutions characterized by envelope expansion with core collapse (EECC), global 3D isothermal perturbation configurations can also be constructed.

What perturbs isotherms? An assessment using fission-track thermochronology and thermal modelling along the Gotthard transect, Central Alps

Abstract Interpretation of low-temperature thermochronological data usually relies on assumptions on the shape of isotherms. Recently, a number of thermal modelling approaches investigate and predict the theoretical influence of topography on isotherms. The application and proof of these predictions is not well confirmed by measured data. Here we present apatite fission-track (AFT) data from samples collected along the Gotthard road tunnel and its corresponding surface line to test these predictions. AFT ages broadly cluster around 6 Ma along the tunnel. No correlation of tunnel ages with superimposed topography is seen, which means that topography-induced perturbation of isotherms under given boundary conditions (topographic wavelength 12 km; relief 1.5 km; exhumation rate 0.45 km Ma −1 ) can be neglected for the interpretation of AFT ages. Thus, in areas characterized by similar topographies and exhumation rates, apparent exhumation rates deduced from the age–elevation relationship (AER) of AFT data need no correction for topography-induced perturbation of isotherms. Three-dimensional (3D) numerical thermal modelling was carried out incorporating thermally relevant parameters and mechanisms, such as topography, geology, thermal conductivities and heat production. Modelling reveals a strong influence on the shape of isotherms caused by spatially variable thermal parameters, especially heat production rates. Therefore, not only topography has to be considered for interpreting low-temperature thermochronological data, but also other parameters like heat production rates. Supplementary material: 1. Electron microprobe analyses, 2. Topography and model extend, 3. Model parameters are all available online at http://www.geolsoc.org.uk/SUP18380 .

Kilometer-scale chemical reaction boundary patterns and deformation in sedimentary rocks

We use three-dimensional (3D) seismic data to image patterns developed by kilometer-scale chemical reaction boundaries to demonstrate that chemical patterns are scaleable phenomena. The patterns develop in biosiliceous marine successions due to the dissolution of opal-A (biogenic silica) and reprecipitation as opal-CT (Crystobalite and Tridymite) during burial. The reaction boundary patterns comprise roughly circular regions where the reaction boundary has preferentially advanced. These regions are up to 2.7 km wide, and c. 50–200 m in height and are termed cells. The cells form by amalgamation with adjacent juvenile cells. They also form by the incorporation of much smaller regions surrounding the cells where the chemical change has already occurred that we term ‘satellites’ (50 m wide). The reaction results in enhanced rates of sediment compaction hence differential advancement of reaction boundaries causes differential subsidence of the overburden, inducing folding and faulting of the overburden above the cellular promontories. We propose three potential mechanisms for the development of kilometer-scale reaction boundary patterns: (a) mass transport of silica by advection (b) perturbation of isotherms as a result of convective or conductive heat transport or (c) establishment of a positive feedback loop between fluid production due to the reaction, hydraulic fracturing and the upward and lateral transport of fluids. This study provides the first insights into how strongly patterned diagenetic reaction boundaries evolve at a basin scale, an initial conceptualization of the potential range of reaction boundary morphologies that could exist in this diagenetic system, and the likely mechanisms that could control them. Furthermore it demonstrates that the discipline of ‘seismic diagenesis’ could represent a completely new approach for the study of chemical diagenetic processes in sedimentary rocks.

Non-Gaussian isocurvature perturbations from inflation

We present a class of very simple inflationary models of two scalar fields which leads to non-Gaussian isothermal perturbations with a ``blue'' spectrum, $n>1.$ One of the models is inspired by supersymmetric theories where light scalar fields naturally acquire masses $\ensuremath{\sim}H$ during inflation. Another model presumes that one of the fields has a nonminimal interaction with gravity $\ensuremath{\xi}R{\ensuremath{\sigma}}^{2}.$ By a slight modification of parameters of these models one can obtain either Gaussian isothermal perturbations, or non-Gaussian adiabatic perturbations with $n>1.$

The unsteady microrotational regime

Using the Cessera model, in which the internal energy depends linearly on the microrotation gradients and non-linearly on the microrotations themselves, the propagation of small isothermal perturbations is investigated. It is shown that for a steady flow of the medium, an unsteady microrotational regime is possible. This effect is interpreted as acoustic emission by the medium.

Axions in inflationary cosmology

The problem of the cosmological constraints on the axion mass is re-examined. It is argued that in the context of inflationary cosmology the constraint m a≳10 −5 eV can be avoided even when the axion perturbations produced during inflation are taken into account. It is shown also that in most axion models the effective parameter ƒ a rapidly changes during inflation. This modifies some earlier statements concerning isothermal perturbations in the axion cosmology. A hybrid inflation scenario is proposed which combines some advantages of chaotic inflation with specific features of new and/or extended inflation. Its implications for theaxion cosmology are discussed.

Thermal radiation from stellar collapse to a black hole.

An analytic solution is presented for the thermal radiation spectrum from a star undergoing catastrophic collapse to a black hole. The matter distribution and gravitational field are modeled by the Oppenheimer-Snyder solution for spherical, homogeneous, dust-ball collapse. The radiation flux emitted during the implosion is calculated assuming the star is initially subjected to a dynamically, isothermal temperature perturbation

Viscous pulsational instability of the transonic region of isothermal geometrically thin accretion discs – I. Analytical results

Viscous instability of the transonic region of the conventional geometrically thin alpha-type accretion disks is examined analytically. For simplicity, isothermal disks and isothermal perturbations are assumed. It is found that when the value of alpha is larger than a critical value the disk is unstable against two types of perturbations. One is local propagating perturbations of inertial acoustic waves. Results suggest the possibility that unstable perturbations develop to overstable global oscillations which are restricted only in the innermost region of the disk. The other is standing growing perturbations localized just at the transonic point. The cause of these instabilities is that the azimuthal component of the Lagrangian velocity variation associated with the perturbations becomes in phase with the variation of the viscous stress force. Because of this phase matching work is done on perturbations, and they are amplified.

Acquisition of angular momentum in the proto-galactic phases

Following Peebles (Ap.J. 155, 393; Astron.Astrophys. 11, 377)and Efstathiou and Silk (Fund.Cosm.Phys. 9, 1) we assume that a developing proto-galaxy of mass M=1011M⊙ gains angular momentum during a first Phase 1 exten ding from recombination to the maximum expansion and then a second Phase 2 from the maximum expansion to a relaxed virialized structure passing through an intermediate Phase I.A very simple model is proposed in which a first mechanism connected with increasing density perturbatio ons leading to a torque ∼ t2/3, is applied to a spherical homogeneus structure. The initial conditions for its dynamical evolution are taken from a cosmological flat model (Ω = 1) with an isothermal perturbation mass spectrum. Phase 2 begins when the proto-galaxy is completely separated from the background and until this Phase it has been recognized that the initial spherical symmetry turns out to be well preserved, provided the angular momentum gained does not exceed 3.6 1073 g cm2 sec−1.

Disturbance of the CBR by Isothermal Perturbations

Following the standard scenario of galaxy formation, density fluctuations with amplitude δ∼10−3 should have been present at the recombination time tR in order that galaxies and clusters of galaxies can be formed. Recent observations of the anisotropy of the cosmic background radiation(CBR), however, indicate that δ is less than 10−4 at tR for adiabatic perturbations in the baryon-dominated universe.

Generation of density perturbations in inflationary cosmology

We discuss several different mechanisms of generation of isothermal (isoinflaton) density perturbations, which can be produced along with the adiabatic (inflaton) perturbations during inflation. It is shown that in many cases the magnitude of isothermal perturbations is sufficiently large for the subsequent galaxy formation. On the other hand, the spectrum of these perturbations may differ considerably from the flat (scale-free) one. It is possible to obtain perturbations with a spectrum which decreases at large (at small) wavelengths, or which has several different maxima, etc. We consider also some nonperturbative mechanisms of generating inhomogeneities during inflation, which lead to the creation of exponentially large strings, domain walls, pancakes, bubbles and other objects. Some astrophysical implications of our results are discussed.

What initial perturbations may be generated in inflationary cosmological models

Isothermal (isoinflaton) perturbations generated in cosmological models at the inflationary stage are discussed. The spectrum of such perturbations has been calculated for the example of a cosmological model with axion-type matter. The possibility of the cut-off of the spectrum at long wavelengths has been shown. This leads to the suppression of large-scale fluctuations of the temperature of the background radiation.

EVOLUTION OF ISOCURVATURE PERTURBATIONS I: PHOTON-BARYON UNIVERSE

The isocurvature perturbation in the photon-baryon universe is comprehensively studied by analytic methods in the framework of the gauge-invariant perturbation theory. In particular the evolutionary behavior of the isocurvature perturbation and its influence on the anisotropy in the cosmic microwave background are examined in detail. The results are compared with those for the adiabatic perturbation and some peculiar features of the isocurvature perturbation are pointed out and their origin is clarified. Besides these studies the ambiguities associated with the definition of non-adiabatic perturbations, especially the so-called isothermal perturbation are critically discussed and a clear definition of isocurvature perturbation is given.

"Isothermal" density perturbations in an axion-dominated inflationary universe.

In inflationary models of the Universe which are axion dominated both adiabatic and isothermal density perturbations arise. We point out that the isothermal perturbations can be more important than the adiabatic perturbations and discuss a model for which this is the case. With isothermal perturbations the spectrum of density perturbations when structure formation begins is flatter and we briefly discuss the implications of this fact. That the amplitude of isothermal fluctuations not be too large provides yet another constraint on models of inflation.

Generation of isothermal density perturbations in the inflationary universe

It is shown that not only adiabatic perturbations of the density but also isothermal density perturbations are generated in the inflationary universe. The magnitude of isothermal perturbations can be sufficiently large for the subsequent galaxy formation. The spectrum of isothermal perturbations can differ considerably from a flat one.

Constraint on the amplitude of isothermal perturbations imposed by an isotropy of the cosmic microwave background radiation

The evolution of initially isothermal perturbations produced in a radiation-dominated universe is investigated until the time of recombination. The ratio of the amplitude of baryon irregularities to that of radiation generated in the course of the evolution of the universe is found. By combining it with the observed upper bound on the anisotropy of the cosmic background radiation, the severe constraint on the amplitude of initially isothermal fluctuations at the time of recombination is defined. This constraint poses a serious difficulty for the theory of galaxy formation based on the isothermal perturbations. 16 references.

Dynamical Evolution of Isothermal Density Perturbations in the Early Universe

Quantitative behaviour of evolution of the initially isothermal perturbations is investigated numerically. It is shown that baryon density contrast decreases slowly in a radiation-dominated epoch, while radiation density perturbation grows in proportion to the scale factor. As a result, contrary to the common understanding, a significant anisotropy on the microwave background is produced. Quantitative results obtained by the numerical analysis make it possible to derive the ratio of the amplitude of baryon irregularities to that of radiation at the time of recombination. Combining it with the observed upper bound on the anisotropy of the cosmic background radiation, we obtain a severe constraint on the amplitude of initially isothermal fluctuations. The resultant constraint casts a serious problem on the theories of galaxy formation based on the isothermal perturbations.

Mechanism of Generating Isothermal Perturbation by a StrongCPNonconservation

A large-scale inhomogeneity of coherent axion field may exist in the early universe. This gives a spatially varying source of strong CP nonconservation and, when coupled to baryon-nonconserving interaction, may lead to generation of the isothermal perturbation of baryon density. A specific mechanism is presented, in which three-body decay of a heavy Majorana lepton gives the additional baryon generation.